Battery acid corrosion continues to creep, even after you clean. The best way to fully prevent this from happening is to bead blast the surrounding area and then seal with silicone or this other paste like circuit board stuff that escapes me right now. Until then, the creep of that corrosion will continue on for a while. Sorry for the bad news, but dealing with old pinball machines that have the same problem, I'm quite experienced with this.
Next best thing if you don't own the proper equipment is to try to stabilize the acid with vinegar, then rubbing alcohol... gently swirling/cleaning with a soft bristled toothbrush. And as someone else mentioned... be careful with the tooth brush. It can whisk away those tiny delicate traces. Then you'll really be screwed as you try to jump everything with tiny wire and solder :-( Which might end up happening a few years from now anyway in an attempt to resurrect the board.
